Advanced MathVery hardHorizontal line touching a parabola once
Advanced Math practice question
The graphs of y = x² − 6x + 10 and y = k, where k is a constant, have exactly one point in common. What is the value of k?
Answer: 1
The parabola's vertex is at x = 3, where y = 9 − 18 + 10 = 1. A horizontal line meets it once only at the vertex.
Common wrong answers
- If you answered 3
- 3 is the x-coordinate of the vertex.
- If you answered 10
- 10 is the y-intercept; y = 10 meets the parabola at x = 0 and x = 6.
- If you answered -1
- −1 has the sign wrong; y = −1 never meets the parabola.
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